Marcoux, Laurent W.Radjavi, HeydarZhang, Yuanhang2022-05-162022-05-162022-06-01https://doi.org/10.1016/j.laa.2022.02.017http://hdl.handle.net/10012/18284The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2022.02.017 © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 licenseIn this paper we consider the problem of determining the maximum dimension of P?(A!B)P, where A and B are unital, semi-simple subalgebras of the set Mn of n⇥n complex matrices, and P 2 M2n is a projection of rank n. We exhibit a number of equivalent formulations of this problem, including the one which occupies the majority of the paper, namely: determine the minimum dimension of the space A\ S−1BS, where S is allowed to range over the invertible group GL(n,C) of Mn. This problem in turn is seen to be equivalent to the problem of finding two automorphisms ↵ and " of Mn for which the dimension of ↵(A)+"(B) is maximised. It is this phenomenon which gives rise to the title of the paper.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalmaximal off-diagonal dimensionminimal intersectionsemi-simple subalgebras of matrix algebrasdispersionArticle